Modeling variance structure of body shape traits of Lipizzan horses

Heterogeneity of variance of growth traits over age is a common issue in estimating genetic parameters and is addressed in this study by selecting appropriate variance structure models for additive genetic and environmental variances. Modeling and partitioning those variances connected with analyzing small data sets were demonstrated on Lipizzan horses. The following traits were analyzed: withers height, chest girth, and cannon bone circumference. The measurements were taken at birth, and at approximately 6, 12, 24, and 36 mo of age of 660 Lipizzan horses born in Croatia between 1948 and 2000. The corresponding pedigree file consisted of 1,458 horses. Sex, age of dam, and stud-year-season interaction were considered fixed effects; additive genetic and permanent environment effects were defined as random. Linear adjustments of age at measuring were done within measuring groups. Maternal effects were included only for measurements taken at birth and at 6 mo. Additive genetic variance structures were modeled by using uniform structures or structures based on polynomial random regression. Environmental variance structures were modeled by using one of the following models: unstructured, exponential, Gaussian, or combinations of identity or diagonal with structures based on polynomial random regression. The parameters were estimated by using REML. Comparison and fits of the models were assessed by using Akaike and Bayesian information criteria, and by checking graphically the adequacy of the shape of the overall (phenotypic) and component (additive genetic and environmental) variance functions. The best overall fit was obtained from models with unstructured error variance. Compared with the model with uniform additive genetic variance, models with structures based on random regression only slightly improved overall fit. Exponential and Gaussian models were generally not suitable because they do not accommodate adequately heterogeneity of variance. Using the unstructured error variance model, the heritability estimates ranged from 0.17 to 0.33 for withers height, 0.07 to 0.27 for chest girth, and 0.14 to 0.30 for cannon bone circumference. This study demonstrated the necessity of accounting for heterogeneity of variances and covariances for body shape traits in Lipizzan horses, and possible difficulties in estimating variance and covariance components when applying more complicated structure models on a small data set. The choice of models depends not only on overall fit but also on the fit of genetic and environmental components.